With the advent of modern data collection devices, intensive longitudinal data are being collected more and more in drug use studies. Intensive longitudinal data have many closely spaced measured occasions, and usually, many variables. In theory, they can provide answers to important questions in drug abuse research. However, in practice, it is not immediately clear what statsitical procedures can be applied to such kind of data to address questions, such as: How does the subjective sensation of withdrawal vary over a day or a week? What is the relationship between mood and drug use? In this project, we propose new semi-varying coefficent mixed models for intensive longitudinal data and time-to-event data. These models possess many valuable features which make them the most appropriate to use for addressing important drug abuse questions and testing key hypotheses in drug use research using intensive longitudinal data. The proposed new models allow effects varying over time and changing across individual subjects, and keep the structure of random error process very flexible. We will propose effective estimation procedures and variable selection procedures for the proposed new models. We will develop software to implement the proposed procedure and assess the performance of the proposed procedures by extensive Monte Carlo simulations. We will also apply the new procedures we have developed to address important drug use questions using empirical data on tobacco, alcohol and marijuana. These are the most widely used substances within the US and have been linked to a myriad of both short and long-term consequences. Findings in this project will help public health researchers to undertand the etiology of drug use and dependence. This understanding can be used to inform drug abuse and treatment efforts.